The integral ∫ π 6 π 3 tan 3 x · sin 2 3 x 2 sec 2 x · sin 2 3 x + 3 tan x · sin 6 x d x is equal to:

Question

The integral &#8747; &#960; 6 &#960; 3 tan 3 x &#183; sin 2 3 x 2 sec 2 x &#183; sin 2 3 x + 3 tan x &#183; sin 6 x d x is equal to:

Aicharya · Accepted Answer

Rearranging, we get, &#8747; &#960; / 6 &#960; / 3 d d x tan 4 x 2 &#183; sin 4 3 x + tan 4 x &#183; d d x sin 4 3 x 2 d x = 1 2 &#8747; &#960; / 6 &#960; / 3 d d x tan 4 x &#183; sin 4 3 x d x = 1 2 tan 4 x &#183; sin 4 3 x &#960; / 6 &#960; / 3 = 1 2 3 4 &#215; 0 - 1 3 4 &#215; 1 = - 1 2 &#215; 1 9 = - 1 18

The integral ∫ π 6 π 3 tan 3 x · sin 2 3 x 2 sec 2 x · sin 2 3 x + 3 tan x ·…

Solution

The integral &#8747; &#960; 6 &#960; 3 tan 3 x &#183; sin 2 3 x 2 sec 2 x &#183; sin 2 3 x + 3 tan x &#183;…

Solution

The integral ∫ π 6 π 3 tan 3 x · sin 2 3 x 2 sec 2 x · sin 2 3 x + 3 tan x ·…